Residents of Nogales advise visitors to avoid “Buenos Aires”, a hillside quarter controlled by violent gangs, where smugglers corral their human cargo in safe houses. At dusk the migrants sneak across a dry river bed and through scrubland for the hazardous trip into Arizona. They are increasingly likely to carry arms or drugs. A resident grumbles that there are more desperate types around. “They will take your socks when they steal your shoes.”

The smugglers may feel increasingly bad-tempered, too. For years a flow of migrants has waxed when the American economy is in rude health, waning only slightly during recessions; it flows north in the spring when agricultural and construction jobs need filling and goes south for Christmas. Where illicit traffic has been heaviest, the migrants’ many footfalls have worn narrow, winding paths into the rocks. But now a big change is visible: the flow of migrants from Latin America to the United States appears to be slumping.

For the third successive year, America’s Border Patrol reports a sharp drop in arrests on and near the frontier. In 2006, the figure dropped 8% to around 1 million. Last year, it dropped by a full fifth. The six months to March showed a year-on-year drop of 17%. In short, and by the imperfect measure of border arrests, the migrant flow today is roughly half the torrent seen in 2000, when 1.64 million arrests were made.

Such figures miss those who cross successfully and recount those detained several times, but they show a clear trend. So does evidence from remittances. Mexico’s central bank reports after years of eye-popping growth, the amount of cash sent home by migrants inside America is falling. Last year such flows were worth $24 billion — more valuable than tourism. But in the first quarter of this year the year-on-year figure was down 2.9%, according to a new report by Goldman Sachs.

Better scrutiny of flows across borders after 2001 probably exaggerated the real rate of growth, so it was bound to taper eventually. But even with that in mind, it is clear migrants really are sending less money home. A poll of migrants across America published by the Inter-American Development Bank in April confirmed fewer are sending money back regularly: in 2006, three-quarters of migrants did, this year only half report doing so. Nor is it only Mexico; Brazil, the second-largest recipient of remittances in the region, saw them slide by 4% last year, to $7.1 billion.

Two factors, each as ugly as the other, probably explain the double downturn in flows of people and money: hostility to migrants, especially undocumented ones, and America’s deepening economic gloom. The impact of the former is plain: state-level laws forbid employers to employ migrants without documents, ever more aggressive raids on businesses that hire such workers, and better technology to share information that will lead to catching them.

High spending on border defenses is the most visible example. The Department of Homeland Security is budgeting $12 billion in the next fiscal year to guard the frontier against job-seekers and the odd mythical terrorist walking to his target. The idea is to use more drones, helicopters, hi-tech sensors and cameras, 20,000 agents on horseback, in jeeps, on bicycles and on foot and of course the big metal fence that unfurls along several hundred miles of dust blown territory. All this discourages migrants, as did the failure last year of the Senate to pass an immigration-reform bill.

No surprise, then, polls show migrants feel less welcome and more worried by xenophobia. Many fear deportation and picking up a criminal record. Those who would once have been sent back now risk jail. As the border gets harder to cross, migrants are pushed further into the hands of smugglers and the natural hazards of the desert.

Hostility and fences would matter less if the economic draw remained strong. Instead America’s economy appears to be in the dumps, even if it avoids a recession. Jobs figures in May showed unemployment had risen to 5.5%. The slump in housing and construction — where many migrants, especially newer arrivals, work — has been especially painful. The Pew Hispanic Center published a study in June showing a 7.5% jobless rate among immigrants, rising to 8.4% among Mexicans and to 9.3% for those who came to the country after 2000. Over 220,000 migrants lost construction jobs last year. And those in work are earning less: wages of Hispanic construction workers tumbled in 2007.

Similarly, as the value of the dollar has tumbled, the attractions of moving to America to work have declined.

For America there is little prospect that the supply of workers from south of the border will dry up; Latin America remains relatively poor and young.

Politically, too, a downturn in migration may be just what is needed to avoid a much nastier xenophobic backlash. One risk, however remote, is a return to the sort of hostility that followed record rates of immigration to America in the early part of the last century. Today in America the foreign-born share of the population is around 13%, not far off the peak of 15% just under a century ago. That peak was followed by much tougher legislation aimed, in particular, at darker-skinned migrants and those from Asia that all but choked off mass immigration for decades, coinciding with an upsurge in protectionism in America and beyond. If anti-foreigner politicians have less to grumble about, the pressure to impose laws that would do long-term damage to migration flows may also lessen.

But even rich countries might worry about a downturn in migration that is more than temporary. Their workforces are aging and shrinking. A recent report from Goldman Sachs notes that as America’s labor force grows more slowly, overall economic output will also slow. It suggests that new migrants have typically added 0.5% to American GDP each year in the past decade, as the foreign-born population has grown to nearly 40 million people.

When ready, America has a big pool of labor to dip into again. Its migration downturn is most likely to be a temporary one.